The 1963 paper by Goldman and Iwahori The space of $p$-adic norms deals with the space of norms on a finite dimensional vector space $E$ over a locally compact complete discrete valuation field $K$. I was wondering if the case when $E$ is infinite dimensional has appeared in the literature.

It looks that in the infinite dimensional case the space of norms should also have similar properties. It should be a metric space, complete, CAT(0), its apartments are isomorphic to a Banach space of bounded sequences with supremum norm...

Question Is there a generalisation of the paper "The space of $p$-adic norms" to the infinite dimensional setting?


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